and heart \(\mathcal {A}(s)= \operatorname{Coh}^{\sharp s}\)  defined in §REF .
For brevity we write (REF ) as \(Z(\gamma )\)  in this section.
The scattering diagram \(\mathcal {D}^{\rm LV}_\psi \)  for \(\psi =0\)  was analyzed in
[1]},
using adapted coordinates \((x=s,y=-\frac{1}{2}(s^2-t^2))\)  such that the
rays \(\Re Z(\gamma )=0\)  are straight lines \(ry+dx-\textnormal {ch}_2=0\)  lying above the parabola \(y=-\frac{1}{2} x^2\) . We shall recast the construction in coordinates \((s,t)\) , which have a more transparent relation to the coordinate \(\tau \)  on the physical slice, and generalize it to any phase \(\psi \in (-\frac{\pi }{2},\frac{\pi }{2})\) . We shall also describe an algorithm for determining which scattering sequences can contribute to the index \(\Omega _{(s,t)}(\gamma )\)  for given charge \(\gamma \) 
and moduli \((s,t)\) , and apply it to compute the Gieseker index \(\Omega _\infty (\gamma )\) 
for small Chern vectors. As a consequence of this algorithm, the Split Attractor Flow Conjecture
holds along the large volume slice.
